Problem: Simplify the following expression: $ k = 1 + \dfrac{-4a + 2}{a + 7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a + 7}{a + 7}$ $ \dfrac{1}{1} \times \dfrac{a + 7}{a + 7} = \dfrac{a + 7}{a + 7} $ Therefore $ k = \dfrac{a + 7}{a + 7} + \dfrac{-4a + 2}{a + 7} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{a + 7 - 4a + 2}{a + 7} $ $k = \dfrac{-3a + 9}{a + 7}$